Method and apparatus for geometric rotor stacking and balancing

ABSTRACT

A computer method or corresponding system for optimally balancing a rotor assembly. The computer system defines a theoretical centerline based on a mathematical model of the rotor assembly. For each disc or component of the rotor assembly, the invention system calculates rotor blade or bolt and washer distribution, based on calculated centerline deviations and angular locations of the discs and effective weights of rotor blade or bolt-and-washer sets. The rotor blade or bolt-and-washer distribution provides locations for placement of the rotor blades or bolts-and-washers so as to offset the centerline deviations and thus correct imbalance of the rotor assembly.

BACKGROUND OF THE INVENTION

A bladed rotor, such as a rotor of a gas turbine engine, includes acentral hub, one or more discs and a plurality of blades secured torespective discs and projecting outward from the hub. The bladed rotorhaving multiple rotor blades rotates about a longitudinal central axis.Because of non-uniform distribution of mass within the rotor assemblyand the blades, it is difficult to achieve a perfect balance for abladed rotor. However, minimizing imbalances within a rotor assembly isessential for minimizing vibration and noise and maximizing theefficiency and performance of the rotor (and turbine engine).

Currently, rotor assemblies are balanced by separately balancing eachdisc or component and aligning respective individual rotor discs orcomponents in the assembly so that the high point of one disc is offsetby the low point of its adjacent disc. The blades are distributed bymass about the theoretical geometric centerline of each disc. The maindrawback of this approach is that it is a trial-and-error method whichdoes not guarantee the optimal alignment of the rotor assembly becausethe separate centerline of each disc or component is not aligned withthe centerline of the rotor assembly. For example, alignment of tworotor discs' centerlines may satisfactorily align those two discs, butintroducing a third disc's high point or low point in the assembly maybe impractical to align with the other two centerlines. The blades maythen be redistributed about each disc in an arbitrary, trial-and-errormanner in the hope of achieving some acceptable balance. A staticbalance machine may be used to add weights to the disc or blades to helpin achieving a rudimentary balance. Consistency and repeatability ismissing in this trial-and-error procedure.

SUMMARY OF THE INVENTION

The present invention addresses the shortcomings of the prior art andprovides a computer method and system for balancing engine modules(e.g., rotor assemblies of a turbine engine).

A method or corresponding apparatus in an exemplary embodiment of thepresent invention calculates a best-fit stack of the discs and theoptimal blade or bolt-and-washer distribution (for rotors withintegrated blades and discs) about the centerline of rotation of therotor assembly for a turbine engine. In particular, the presentinvention defines an actual centerline of a geometrical/mathematicalmodel of a rotor assembly (module) as a whole. Based on the definedcenterline, the system calculates a centerline deviation of each disc orcomponent of the rotor assembly. Calculating the centerline deviationincludes measurement characteristics of a set of rotor blades, a disc, ashaft, a hub, and/or a spacer. For each of these measurements, thefollowing information is calculated: roundness, flatness, concentricity,concentricity angle, runout, runout angle, perpendicularity,perpendicularity angle, perpendicular plane deviation, centerlinedeviation, centerline deviation angle, biplane deviation, and biplanedeviation angle. After calculating the best fit centerline deviation foreach component, the invention system determines an angular location ofthe component of the turbine engine.

Next, the invention system determines the centerline deviation and angleof each disc based on the centerline of both ends of the subject moduleas stacked and determines disc blade distribution within the turbineengine based on the calculated centerline deviation and the angularlocation of the disc/component of the turbine engine. Determining rotorblade distribution includes weighing of each rotor blade for thedisc/component of the turbine engine by either pan weight or momentweight, as appropriate.

Each rotor blade of the set of rotor blades for a given disc may beidentified by a number label (indicator) and a blade weight. Further,determining the blade distribution may also include computing a rotorblade distribution in order to offset the centerline deviation. Theprocess of offsetting the discs' centerline deviation optimally balancesthe rotor assembly/module of the turbine engine.

This rotor blade distribution per disc is displayed to a user in both anumerical and graphical format. After determining the rotor bladedistribution, the rotor blades may be assembled on each disc of theturbine engine using the displayed information. The resulting rotorassembly is then verified against the computer model prediction. If theblades are integral to their discs, then the distribution is in the formof bolts and washers (bolts connect discs to each other in theassembly). It should be understood that this method or correspondingapparatus in an exemplary embodiment may be applied to a low-pressureturbine, intermediate-pressure turbine, a high pressure turbine, alow-pressure compressor, an intermediate-pressure compressor, a highpressure compressor, a combination of rotors, or a combination of rotorswith their respective shafts or hubs.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing will be apparent from the following more particulardescription of example embodiments of the invention, as illustrated inthe accompanying drawings in which like reference characters refer tothe same parts throughout the different views. The drawings are notnecessarily to scale, emphasis instead being placed upon illustratingembodiments of the present invention.

FIG. 1 is a side view of a system embodying the present invention;

FIG. 2A is a plane view of a high pressure compressor and turbinemodules;

FIG. 2B is a plane view of a low pressure compressor and turbinemodules;

FIG. 2C is a plane view of a low pressure shaft and low-pressurecompressor and turbine modules, including a pair of bearing housings;

FIG. 2D is a flow diagram of an example process used to determine thepredicted rotor assembly and rotor blade distribution;

FIG. 3 is a flow diagram of an example process of calculating rotorblade or bolt-and-washer distribution for a disc of a turbine enginerotor according to the present invention;

FIG. 4 is a schematic diagram of a rotor blade or bolt-and-washerdistribution about a given disc;

FIG. 5 is a flow diagram of an example process of displaying rotor bladeor bolt-and-washer distribution information to a user according to thepresent invention;

FIG. 6 is a flow diagram of an example process of mounting a rotormodule and verifying the straightness of the module in the presentinvention;

FIG. 7 is a screen view diagram of a rotor disc stacking process andblade or bolt-and-washer distribution employing the present invention;

FIG. 8 is a flow diagram illustrating an example process of determininga predicted vibration of a rotor module and set of rotor blades utilizedin embodiments of the present invention;

FIG. 9 is a schematic diagram of a rotor assembly on a balancing machineas employed by the present invention process of FIG. 10; and

FIG. 10 is a flow diagram illustrating an example process of balancing arotor assembly.

DETAILED DESCRIPTION OF THE INVENTION

A description of preferred embodiments of the invention follows.

FIG. 1 is a system 100 of the present invention for calculating a rotorblade or bolt-and-washer distribution (or disc thereof) or othercomponent 140 that achieves optimal balance throughout a module (rotorassembly) in a turbine engine. It is useful to note that calculating therotor blade or bolt-on-washer distribution is typically performed insuch a manner as to have an optimal straight build of a rotor assembly.The system 100 uses a determination module 105 for performingcalculations. Within the determination module 105, there is a digitalprocessing unit (with CPU) 110, a display monitor 115, a printer 120, abar code reader 122, and input devices 125 and 130, such as a keyboardor mouse. The determination module 105 interacts with at least onesensor or probe 145 located on a vertical gage 135. The vertical gage135 has a disc, disc and blade assembly, or other component 140 on astand in such a manner as to allow at least one sensor or probe 145 tomake measurements. These measurements are transmitted to thedetermination module 105 where they are used for calculating a best fitstack of discs and balanced module rotor blade or bolt-and-washerdistribution according to the principles of the present invention. Thedetermination module 105 having received the sensor measurementinformation/data from at least one sensor or probe 145, calculates adisc or component (e.g. shafts, hub, etc.) location, with respect to adefined centerline for assembly purposes.

In addition, the system 100 uses a determination module 150 forperforming measurements. Within the determination module 150, there is adigital processing unit (with CPU) 160, a display monitor 170, a printer175, and input devices 165 and 166, such as a keyboard or mouse. Thedetermination module 150 interacts with either a pan weight scale 180 ora moment weight scale 185. The pan weight scale 180 determines theweight of blades, except in those instances where a moment weight isrequired. If the moment weight is required, the moment weight scale 185calculates the moment weight. After calculating the weight, the CPU 160stores the calculated/measured weight using an identification numberassociated to a specific disc. A bar code printer 190 identifies(produces) a barcode and the identification number that are associatedwith the specific disc. Bar code reader 122 reads the printed bar codeas input for determination module 105.

FIG. 2A shows a high-pressure spool 210 of a gas turbine. Thehigh-pressure spool 210 includes a high-pressure compressor 220, ahigh-pressure turbine 230, and a high-pressure shaft 240. Thehigh-pressure compressor 220 includes a plurality or rotor blades 220 a. . . 220 n, each set of blades being carried by a respective disc 213 a. . . n. The high-pressure turbine 230 includes a plurality of rotorblades 230 a . . . 230 n, each set of blades being carried by arespective disc 230 a . . . n.

FIG. 2B shows a low-pressure spool 250 of a gas turbine. Thelow-pressure spool 250 includes a low-pressure compressor 260, alow-pressure turbine 270, and a low-pressure shaft 280. The low-pressureshaft 280 rotates within the high-pressure shaft 240. In some enginedesigns, the high-pressure shaft 240 and the low-pressure shaft 280 isthe same shaft. It is useful to note that in some engine designs anintermediate shaft compressor (not shown) and discs may also be used.

FIG. 2C generally shows a low-pressure shaft 240 and a low-pressurecompressor 260 extending through a pair of bearing housings 245. Theproper alignment of a rotor assembly with the centerline through thebearings can reduce the vibration and imbalance of the rotor assemblyand turbine engine. One such useful component to align is the disc 213 ncarrying the plurality of rotor blades 220 or rotor blade fan 24. An oilcirculation system delivers lubricating oil to lubricate the bearings(not shown) within the respective bearing housings 245, wherein the oilflows through the bearings for drainage to a sump, not shown, within alower region of the bearing housing 245. As will be readily understood,proper alignment of components of each bearing housing 245 willsubstantially reduce the onset of oil leakage. Further, proper alignmentof the dynamic and static structures of each bearing can reduce rapidwear of the seal structures. Alignment of the disc 213 n carrying theplurality of rotor blades 220 or blade fan 24 is as follows:

Characteristic information of each part (e.g., disc 213, rotor blades220, etc.) is measured and input to a software program (e.g.,“SuperStack” by AXIAM, Incorporated of Gloucester, Mass.) of thedetermination module 105 of FIG. 1. The software program uses the inputcharacteristic measurements to generate output characteristicmeasurements for aligning discs 213 and the plurality of rotor blades220. In particular, the software program outputs correct balancinginformation in the form of a rotor blade or bolt-and-washerdistribution. The rotor blade or bolt-and-washer distribution iscomputed by 1) calculating a centerline deviation of each rotor discwith respect to the centerline of the rotor assembly (module) as a whole(from end to end); 2) calculating an angular location of each rotordisc; and 3) determining the rotor blade or bolt-and-washer distributionbased on the centerline deviation and angular location of each rotordisc.

Referring now to the centerline deviation, the measurementcharacteristics include those of a set of rotor blades, a disc, a shaft,a hub, and a spacer. For each part measurement, the software programmathematically levels and centers the part. The software program buildsa mathematical model for the parts as hypothetically placed together toform a rotor assembly or module. The software program defines from endto end (including bearings or journals) an assembly model theoreticalcenterline. Using the theoretical centerline, the software programcalculates geometric measurements of each part including: roundness,flatness, concentricity, concentricity angle, runout, runout angle,perpendicularity, perpendicularity angle, perpendicular plan deviation,centerline deviation, centerline deviation angle, biplane deviation andbiplane deviation angle. Using these measurement characteristics, arotor blade or bolt-and-washer distribution for the plurality of rotorblades in the subject rotor assembly (module) is calculated. Inparticular, the software program calculates the location of each part inspace. Using a known weight of each part (user input data such as grossweight, moment weight or manufacturing weight, e.g., from bar codereading in FIG. 1) and the foregoing measurement characteristics(calculated geometric measurements), the software program calculates ablade or bolt-and-washer distribution which offsets centerlinedeviations and balances the overall subject rotor assembly. In apreferred embodiment, this is accomplished using Applicants'mathematical formula/process which is illustrated in FIG. 2D.

FIG. 2D is an information flow diagram 282 that represents themathematical formulas used in rotor assembly and blade orbolt-and-washer distribution of the present invention. Morespecifically, the process calculates a straight rotor assembly against acenterline between bearing journals. At step 284, the process inputsdata that relates to part and other information. The part informationincludes height, diameter, weight, center of gravity location, probelocation, number of bolt holes, bolt hole radius, and individual bladeweight whereas other information includes rotor speed, part with bearingjournal, number of blades, bolt weight, and washer weight. Afterreceiving the data input, step 286 calculates the best fit centerlinefor each part in the assembly. The calculation uses HomogeneousTransformation Matrix (HTM) mathematics for each part from establisheddatum to predict a straight assembly. In particular, the HTM uses probelocations and number of bolt holes data received in step 284 allowingthe process to calculate the centerline deviation and angular locationof each component of the assembly in step 288. After calculating thecenterline and angular location, the process creates a new centerlineand angle of each part at step 290 using the probe locations and numberof bolt holes. The process mathematically translates the centerline ofthe assembly to two bearing journal centerlines in such a manner as tocreate a new centerline and angle for each part. At step 292, theprocess mathematically calculates balance and angle for each part basedon a computed deviation of each part from the journal centerline. Incalculating the balance and angle, the process uses the following data:centerline deviation, centerline deviation angle, center of gravitylocation, weight, height, and diameter. Next, at step 294 the processcomputes a blade distribution or bolt and washer distribution based onthe part centerline, center of gravity and weight. In computing theblade or bolt and washer distribution, the process uses the followingdata: centerline deviation, centerline deviation angle, center ofgravity location, part weight, and blade weight. Next, the processcomputes the balance of the assembled rotor (step 296) and then aprojected rotor vibration (step 298). In computing the rotor balance andvibration, the process uses the following data: balance deviation ofeach plane, rotor weight and rotor speed. In this way, the processpredicts rotor assembly and rotor blade distribution.

It should be understood by one skilled in the art that the alignment ofa plurality of rotor blades or bolts-and-washers 220 n may be applied toa low-pressure turbine, an intermediate-pressure turbine, ahigh-pressure turbine, a low-pressure compressor, anintermediate-pressure compressor, or a high-pressure compressor.

FIG. 3 is a flow diagram 300 illustrating an example process ofcomputing a blade or bolt-and-washer distribution for a disc of aturbine engine according to the present invention. After defining themodel centerline, the blade or bolt-and-washer distribution process 300calculates a centerline deviation and an angular location of each rotordisc or component of the turbine engine (step 305). Further, the processcomputes a blade distribution for each rotor blade in a set of rotorblades of a given disc (steps 310 a, 310 b and 315). Next, the processcalculates the weight distribution based on the centerline deviation andangular location of the given disc (as calculated in 305) and the weighteffects of each blade or bolt-and-washer in the set.

FIG. 4 is a schematic diagram of a rotor blade or bolt-and-washerdistribution 400 for a given disc 213 of FIG. 2A. A turbine engine rotordisc 405 is seen in such a manner as to view the location of rotorblades or bolts-and-washers 410, 415, and 420. Rotor blade 410 islabeled or identified as blade number 26 and is shown in slot or bladelocation number 1 of the subject disc. Rotor blade 415 is shown in bladelocation number 2 and has identifier number 42. Similarly rotor blade420 is shown in slot/blade location 3 and identified as blade number 6.The placement of each rotor blade is based on the rotor bladedistribution described above. In particular, the rotor blades 410, 415,and 420 are positioned (assigned a slot/blade position) in such a way asto geometrically balance the given rotor component or disc to thetheoretical centerline of the rotor assembly by offsetting the disc'scalculated centerline deviation and angular location with the weight ofeach rotor blade.

FIG. 5 is a flow diagram 500 illustrating an example displaying processof blade or bolt-and-washer distribution information. Before displayingblade or bolt-and-washer distribution information, the distributioninformation is calculated as described above. At step 505, the processcalculates a centerline deviation and angular location for each rotordisc or component of a turbine engine. For each rotor disc of a rotorassembly, the process computes a blade distribution (loop 510 a through510 b). Next, at step 515, the process computes blade or bolt-and-washerdistribution based on (a) the centerline deviations and angularlocations of components/discs of the turbine engine as calculated instep 505, and (b) weight effects of the blades or bolts-and-washers perblade or bolt position. From the results of step 515, the process 500displays numerical and graphical results illustrating blade position perdisc on a display monitor (step 520).

FIG. 6 is a flow diagram 600 of an example process of verifying asubject module (e.g., rotor assembly of a turbine engine) against theinitial predictive mathematical model. The process mounts the subjectmodule on a gage (step 610). Next, as measured by the gage, the processcompares location and orientation of the module to that of themathematical model. Based on the comparison, the process verifies thestraightness of the subject module to the predictive mathematical model(step 615).

FIG. 7 is a schematic diagram of a rotor disc stacking and balancing(blade distribution) output 700 of a preferred embodiment. A set ofrotor discs 705, 715, and 725 are shown with their respective individualor part center 710, 720, and 730, respectively. The rotor assembly as awhole has a defined centerline shown at 735. The centerline 735 depictsa theoretical model centerline, a centerline deviation, and an angularlocation of each rotor disc 705, 715, and 725. Rotor blade orbolt-and-washer distribution are indicated by balance points (shadeddots) which result from the above described computation relating tocalculated centerline deviations and the angular locations of discs toweight effects of rotor blades or bolts-and-washers at blade locationsof the disc. The rotor blade or bolt-and-washer distribution allows foran aligned stacking of each rotor disc 705, 715 and 725.

It is useful to note that using the foregoing output 400, 700, (e.g.,blade or bolt-and-washer distribution information of FIG. 4 and rotordisc stacking and balancing of FIG. 7) one is able to optimally assemblea module (e.g., rotor assembly) of the turbine engine.

FIG. 8 is a flow diagram 800 illustrating an example process ofdetermining a predicted vibration of a module assembled according to theabove. The process 800 receives input of a manufacturer-specifiedoperating speed of the rotor. Receiving the specified operating speedallows one to adjust for vibration using known techniques given theresults of process 800 such as the weight distribution of disc 213,associated blade sets or bolts-and-washers and other rotor components(resulting from the output 700 of FIG. 7). Step 805 measures andcalculates a centerline deviation and an angular location for each rotordisc of the assembled engine. Next, the process makes a computation ofthe blade or bolt-and-washer distribution and a determination of thepredicted vibration for each rotor disc (steps 810 through 820). Inparticular, step 815 computes a blade or bolt-and-washer distributionbased on the centerline deviation and angular location of the discand/or component with respect to the measured centerline of the turbineengine (as calculated in step 805) and offset weight effects of theblades in terms of displacement and velocity. After the last iterationof step 820, the process determines a predicted imbalance of a set ofrotor blades or bolts-and-washers for each rotor disc 213. It is usefulto note the rotor vibrations may be determined while the turbine is inan operational state (. i.e., test cell). Next, the process determinesthe predicted vibration of a module assembly (step 825). That is,predicted vibration enables one to determine in advance of operation ifthe subject rotor assembly does not meet vibration threshold/criteria.

FIG. 9 is a schematic diagram of a balancing machine assembly 900.Specifically, a balancing machine 905 contains a module 910 for balancetesting. More specifically, the module 910 is installed in the balancingmachine 905 for verification of an initial unbalance in two differentplanes (e.g., left and right plane). Verification is performed using themathematical model described above.

FIG. 10 is a flow diagram illustrating an example process 1000 ofbalancing a rotor assembly. After beginning (step 1005), the processinstalls a completed rotor assembly onto a balancing machine (step 1010)such as that illustrated in FIG. 9. Next, the process measures a leftplane and a right plane of the rotor assembly to check for anyunbalances or imbalances (step 1015). After measuring the planes, theprocess verifies the actual balance by comparing the actual values withpreviously computed predicted balance values (step 1020). Afterverifying the actual balance, the process 1000 completes a final trimbalance on the left and right planes as indicated by the verificationprocess (step 1025).

1. A method for correcting imbalance of a rotor assembly for a turbineengine, comprising the computer implemented steps of: defining acenterline of a rotor assembly based on a mathematical model of therotor assembly, the rotor assembly being formed of discs and components,each disc for carrying a respective set of rotor blades orbolts-and-washers; for each disc and component of the rotor assembly,calculating a centerline deviation and an angular location of the discand component, resulting in a plurality of centerline deviations andangular locations of the discs and components of the rotor assembly; anddetermining rotor blade or bolt-and-washer distribution throughout therotor assembly based on (a) the plurality of calculated centerlinedeviations and the angular locations of the discs and components of therotor assembly and (b) respective weight of each rotor blade orbolt-and-washer, the rotor blade or bolt-and-washer distributionproviding rotor blade or bolt-and-washer locations which offset thecenterline deviations by weight and result in a balanced rotor assembly.2. The method of claim 1, wherein the step of determining rotor blade orbolt-and-washer distribution includes weighing a set of rotor blades orbolts-and-washers of the turbine engine by pan weight or moment weight.3. The method of claim 1, further comprising marking each rotor blade orbolt-and-washer with an identifying number and the blade location abouta respective disc.
 4. The method of claim 1, wherein the step ofdetermining rotor blade or bolt-and-washer distribution further includesfor each disc, computing the locations of respective rotor blades orbolts-and-washers in order to offset the centerline deviation of thedisc.
 5. The method of claim 1, further including displaying anindicator of the determined rotor blade or bolt-and-washer distributionto a user.
 6. The method of claim 5, wherein the indicator of thedetermined rotor blade or bolt-and-washer distribution is displayed innumerical format.
 7. The method of claim 5, wherein the indicator of therotor blade or bolt-and-washer distribution is displayed in graphicalformat.
 8. The method of claim 5, further including assembling the rotorblades or bolts-and-washers on the respective disc based on thedisplayed information.
 9. The method of claim 8, further includingverifying the rotor assembly resulting from the assembly, against themathematical model.
 10. The method of claim 1, wherein the step ofcalculating includes determining measurement characteristics in anycombination of: roundness, flatness, concentricity, concentricity angle,runout, runout angle, perpendicularity, perpendicularity angle,perpendicular plane deviation, centerline deviation, centerlinedeviation angle, biplane deviation and biplane deviation angle.
 11. Themethod of claim 1, wherein the rotor assembly is assembled into any of alow-pressure turbine, an intermediate-pressure turbine, a high-pressureturbine, a low-pressure compressor, an intermediate-pressure compressor,or a high-pressure compressor.
 12. The method of claim 11, wherein thestep of defining a centerline of the rotor assembly includes determininga centerline generated between bearing journals.
 13. A computer systemfor correcting imbalance of a rotor assembly for a turbine engine,comprising: a definition module configured to define a centerline of arotor assembly based on a mathematical model of the rotor assembly, therotor assembly being formed of discs and components, each disc forcarrying a respective set of rotor blades or bolts-and-washers; acalculation module configured to calculate a centerline deviation and anangular location of the disc and component, resulting in a plurality ofcenterline deviations and angular locations of the discs and componentsof the rotor assembly for each disc and component of the rotor assembly;and a determination module configured to determine rotor blade orbolt-and-washer distribution throughout the rotor assembly based on (a)the plurality of calculated centerline deviations and the angularlocations of the discs and components of the rotor assembly and (b)respective weight of each rotor blade or bolt-and-washer, the rotorblade or bolt-and-washer distribution providing rotor blade orbolt-and-washer locations which offset the centerline deviations andresult in an optimally balanced rotor assembly.
 14. The computer systemof claim 13 wherein the determination module weighs a set of rotorblades or bolts-and-washers of the turbine engine by pan weight ormoment weight.
 15. The computer system of claim 13, further comprising amarking module configured to mark each rotor blade or bolt-and-washerwith an identifying number and the location about a respective disc. 16.The computer system of claim 13 wherein the determination modulecomputes the locations of respective rotor blades or bolts-and-washersin order to offset the centerline deviation of the disc for each disc.17. The computer system of claim 13 wherein a display module isconfigured to display an indicator of the determined rotor blade orbolt-and-washer distribution to a user.
 18. The computer system of claim17, wherein the indicator of the determined rotor blade orbolt-and-washer distribution is displayed in numerical format.
 19. Thecomputer system of claim 17, wherein the indicator of the rotor blade orbolt-and-washer distribution is displayed in graphical format.
 20. Thecomputer system of claim 17, further comprising an assembly moduleconfigured to assemble the rotor blades or bolts-and-washers on therespective disc based on the displayed information.
 21. The computersystem of claim 20, further including a verification module configuredto verify the rotor assembly resulting from the assembly, against themathematical model.
 22. The computer system of claim 13, wherein thecalculation module is further configured to determine measurementcharacteristics in any combination of: roundness flatness,concentricity, concentricity angle, runout, runout angle,perpendicularity, perpendicularity angle, perpendicular plane deviation,center-line deviation, centerline deviation angle, biplane deviation andbiplane deviation angle.
 23. The computer system of claim 13, whereinthe rotor assembly is assembled into any of a low-pressure turbine, anintermediate-pressure turbine, a high-pressure turbine, a low-pressurecompressor, and intermediate-pressure compressor, or a high-pressurecompressor.
 24. The computer system of claim 13, wherein a definitionmodule is further configured to determine a centerline generated betweenbearing journals of the rotor assembly.
 25. The computer system of claim13, wherein the rotor assembly is assembled into a low shaft,intermediate shaft, or high shaft, respectively to meet target vibrationthreshold/criteria.